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A038050 Number of labeled rooted trees with 3-colored leaves. 2
3, 6, 45, 504, 7785, 153468, 3681909, 104126256, 3392064945, 125089571700, 5151335388309, 234322765501608, 11668410187187481, 631335472193760012, 36881146426978035765, 2313552152470193124192, 155107536736245864549345 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.83)

LINKS

Table of n, a(n) for n=1..17.

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

FORMULA

Divides by n and shifts left under exponential transform.

E.g.f.: 2*x - LambertW(-x*exp(2*x)). - Vladeta Jovovic, Mar 09 2003

a(n) = Sum_{k=0..n} (binomial(n, k)*2^k*(n-k)^(n-1)).

a(n) ~ sqrt(1+LambertW(2*exp(-1))) * (2*exp(-1)/LambertW(2*exp(-1)))^n * n^(n-1). - Vaclav Kotesovec, Oct 05 2013

MATHEMATICA

Rest[CoefficientList[Series[2*x-LambertW[-x*E^(2*x)], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 05 2013 *)

CROSSREFS

Cf. A000169, A029857.

Cf. A038049.

Sequence in context: A203434 A076170 A137775 * A194080 A261841 A197884

Adjacent sequences:  A038047 A038048 A038049 * A038051 A038052 A038053

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)